Respuesta :
Answer:
The equation of the least-squares regression line is [tex]y=29.412x+294.348[/tex].
Step-by-step explanation:
Consider the provided information.
If we know the mean and standard deviation for x and y, along with the correlation (r), we can calculate the slope b and the starting value a with the following formulas:
[tex]y-\bar y=\frac{r\sigma_x}{\sigma_x}(x-\bar x)[/tex]
It is given that The average SAT score was 912 with a standard deviation of 180. The average ACT score was 21 with a standard deviation of 5. The correlation between the two variables equals 0.817.
Therefore, substituent [tex]\bar x=21, \sigma_x=5, \bar y=912, \sigma_y=180\ and\ r=0.817[/tex] in above formula.
[tex]y-912=\frac{0.817\times 180}{5}(x-21)[/tex]
[tex]y-912=0.817\times 36(x-21)[/tex]
[tex]y-912=29.412(x-21)[/tex]
[tex]y=29.412x-617.652+912[/tex]
[tex]y=29.412x+294.348[/tex]
The equation of the least-squares regression line is [tex]y=29.412x+294.348[/tex].
